intellecton/papers/project_paper_2_neuroscience/references/Bastos2012.txt

Canonical microcircuits for predictive coding

Andre M. Bastos1,2,6, W. Martin Usrey1,3,4, Rick A. Adams8, George R. Mangun2,3,5, Pascal
Fries6,7, and Karl J. Friston8

1Center for Neuroscience, University of California-Davis, Davis, CA 95618 USA. 2Center for Mind
and Brain, University of California-Davis, Davis, CA 95618 USA. 3Department of Neurology,
University of California-Davis, Davis, CA 95618 USA. 4Department of Neurobiology, Physiology
and Behavior, University of California-Davis, Davis, CA 95618 USA. 5Department of Psychology,
University of California-Davis, Davis, CA 95618 USA. 6Ernst Strüngmann Institute (ESI) for
Neuroscience in Cooperation with Max Planck Society, Deutschordenstraße 46, 60528 Frankfurt,
Germany. 7Donders Institute for Brain, Cognition and Behaviour, Radboud University Nijmegen,
Kapittelweg 29, 6525 EN Nijmegen, Netherlands. 8The Wellcome Trust Centre for Neuroimaging,
University College London, Queen Square, London WC1N 3BG, UK.

Summary

This review considers the influential notion of a canonical (cortical) microcircuit in light of recent
theories about neuronal processing. Specifically, we conciliate quantitative studies of
microcircuitry and the functional logic of neuronal computations. We revisit the established idea
that message passing among hierarchical cortical areas implements a form of Bayesian inference –
paying careful attention to the implications for intrinsic connections among neuronal populations.
By deriving canonical forms for these computations, one can associate specific neuronal
populations with specific computational roles. This analysis discloses a remarkable
correspondence between the microcircuitry of the cortical column and the connectivity implied by
predictive coding. Furthermore, it provides some intuitive insights into the functional asymmetries
between feedforward and feedback connections and the characteristic frequencies over which they
operate.

Keywords

neuronal; connectivity; cortical; microcircuit; computation; predictive coding; free energy
principle; gamma oscillations; beta oscillations

Introduction

The idea that the brain actively constructs explanations for its sensory inputs is now
generally accepted. This notion builds on a long history of proposals that the brain uses
internal or generative models to make inferences about the causes of its sensorium
(Helmholtz, 1860; Gregory 1968, 1980; Dayan et al., 1995). In terms of implementation,
predictive coding is, arguably, the most plausible neurobiological candidate for making
these inferences (Srinivasan et al., 1982; Mumford, 1992; Rao and Ballard, 1999). This
review considers the canonical microcircuit in light of predictive coding. We focus on the
intrinsic connectivity within a cortical column and the extrinsic connections between

Correspondence: Karl Friston The Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College London, 12
Queen Square, London, WC1N 3BG, UK. Tel (44) 207 833 7454 k.friston@ucl.ac.uk.

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Published in final edited form as:
Neuron. 2012 November 21; 76(4): 695–711. doi:10.1016/j.neuron.2012.10.038.

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columns in different cortical areas. We try to relate this circuitry to neuronal computations
by showing the computational dependencies – implied by predictive coding – recapitulate
the physiological dependencies implied by quantitative studies of intrinsic connectivity. This
issue is important as distinct neuronal dynamics in different cortical layers are becoming
increasingly apparent (de Kock et al., 2007; Sakata and Harris, 2009; Maier et al., 2010;
Bollimunta et al., 2011). For example, recent findings suggest that the superficial layers of
cortex show neuronal synchronization and spike-field coherence predominantly in the
gamma frequencies, while deep layers prefer lower (alpha or beta) frequencies (Roopun et
al., 2006, 2008; Maier et al., 2010; Buffalo et al., 2011). Since feedforward connections
originate predominately from superficial layers and feedback connections from deep layers,
these differences suggest that feedforward connections use relatively high frequencies,
compared to feedback connections, as recently demonstrated empirically (Bosman et al.,
2012). These asymmetries call for something quite remarkable: namely, a synthesis of
spectrally distinct inputs to a cortical column and the segregation of its outputs. This
segregation can only arise from local neuronal computations that are structured and
precisely interconnected. It is the nature of this intrinsic connectivity – and the dynamics it
supports – that we consider. The aim of this review is to speculate about the functional roles
of neuronal populations in specific cortical layers in terms of predictive coding. Our long-
term aim is to create computationally informed models of microcircuitry that can be tested
with dynamic causal modelling (David et al., 2006; Moran et al., 2008, 2011).

This review comprises three sections. We start with an overview of the anatomy and
physiology of cortical connections – with an emphasis on quantitative advances. The second
section considers the computational role of the canonical microcircuit that emerges from
these studies. The third section provides a formal treatment of predictive coding and defines
the requisite computations in terms of differential equations. We then associate the form of
these equations with the canonical microcircuit to define a computational architecture. We
conclude with some predictions about intrinsic connections and note some important
asymmetries in feedforward and feedback connections that emerge from this treatment.

The anatomy and physiology of cortical connections

This section reviews laminar-specific connections that underlie the notion of a canonical
microcircuit (Douglas et al., 1989; Douglas and Martin, 1991, 2004). We first focus on
mammalian visual cortex and then consider whether visual microcircuitry can be generalized
to a canonical circuit for the entire cortex. Both functional and anatomical techniques have
been applied to study intrinsic (intracortical) and extrinsic connections. We will emphasise
the insights from recent studies that combine both techniques.

Intrinsic connections and the canonical microcircuit

The seminal work of Douglas and Martin (1991), in the cat visual system, produced a model
of how information flows through the cortical column. Douglas and Martin recorded
intracellular potentials from cells in primary visual cortex during electrical stimulation of its
thalamic afferents. They noted a stereotypical pattern of fast excitation, followed by slower
and longer-lasting inhibition. The latency of the ensuing hyperpolarisation distinguished
responses in supragranular and infragranular layers. Using conductance-based models, they
showed that a simple model could reproduce these responses. Their model contained
superficial and deep pyramidal cells with a common pool of inhibitory cells. All three
neuronal populations received thalamic drive and were fully interconnected. The deep
pyramidal cells received relatively weak thalamic drive but strong inhibition (Figure 1).
These interconnections allowed the circuit to amplify transient thalamic inputs to generate
sustained activity in the cortex, while maintaining a balance between excitation and
inhibition, two tasks that must be solved by any cortical circuit. Their circuit, although based

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on recordings from cat visual cortex, was also proposed as a basic theme that might be
present and replicated, with minor variations, throughout the cortical sheet (Douglas et al.,
1989).

Subsequent studies have used intracellular recordings and histology to measure spikes (and
depolarisation) in pre and post-synaptic cells, whose cellular morphology can be determined.
This approach quantifies both the connection probability – defined as the number of
observed connections divided by total number of pairs recorded – and connection strength –
defined in terms of post-synaptic responses. Thomson et al (2002) used these techniques to
study layers 2 to 5 (L2 to L5) of the cat and rat visual systems. The most frequently
connected cells were located in the same cortical layer, where the largest interlaminar
projections were the ‘feedforward’ connections from L4 to L3 and from L3 to L5. Excitatory
reciprocal ‘feedback’ connections were not observed (L3 to L4) or less commonly observed
(L5 to L3), suggesting that excitation spreads within the column in a feedforward fashion.
Feedback connections were typically seen when pyramidal cells in one layer targeted
inhibitory cells in another (see Thomson and Bannister, 2003 for a review).

While many studies have focused on excitatory connections, a few have examined inhibitory
connections. These are more difficult to study, because inhibitory cells are less common
than excitatory cells, and because there are at least seven distinct morphological classes
(Salin and Bullier, 1995). However, recent advances in optogenetics have made it possible
to more easily target inhibitory cells: Kätzel and colleagues combined optogenetics and
whole-cell recording to investigate the intrinsic connectivity of inhibitory cells in mouse
cortical areas M1, S1, and V1 (Kätzel et al., 2010). They transgenically expressed
channelrhodopsin in inhibitory neurons and activated them, while recording from pyramidal
cells. This allowed them to assess the effect of inhibition as a function of laminar position
relative to the recorded neuron.

Several conclusions can be drawn from this approach (Kätzel et al., 2010): first, L4
inhibitory connections are more restricted in their lateral extent, relative to other layers. This
supports the notion that L4 responses are dominated by thalamic inputs, while the remaining
laminae integrate afferents from a wider cortical patch. Second, the primary source of
inhibition originates from cells in the same layer, reflecting the prevalence of inhibitory
intralaminar connections. Third, several interlaminar motifs appeared to be general – at least
in granular cortex: principally, a strong inhibitory connection from L4 onto supragranular
L2/3 and from infragranular layers onto L4. For more information on the cell-type
specificity of inhibitory connections, see Yoshimura and Callaway, (2005). Figure 2
provides a summary of key excitatory and inhibitory intralaminar connections.

Microcircuits in the sensorimotor cortex

Do the features of visual microcircuits generalize to other cortical areas? Recently, two
studies have mapped the intrinsic connectivity of mouse sensory and motor cortices: Lefort
and colleagues (2009) used multiple whole-cell recordings in mouse barrel cortex to
determine the probability of monosynaptic connections – and the corresponding connection
strength. As in visual cortex, the strongest connections were intralaminar and the strongest
interlaminar connections were the ascending L4 to L2, and descending L3 to L5.

One puzzle about canonical microcircuits is whether motor cortex has a local circuitry that is
qualitatively similar to sensory cortex. This question is important because motor cortex lacks
a clearly defined granular L4 (a property that earns it the name “agranular cortex”). Weiler
and colleagues combined whole-cell recordings in mouse motor cortex with photo-
stimulation to uncage Glutamate (Weiler et al., 2008). This allowed them to systematically
stimulate the cortical column in a grid – centred on the pyramidal neuron from which they

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recorded. By recording from pyramidal neurons in L2-6 (L1 lacks pyramidal cells), the
authors mapped the excitatory influence that each layer exerts over the others. They found
that the L2/3 to L5A/B was the strongest connection – accounting for one-third of the total
synaptic current in the circuit. The second strongest interlaminar connection was the
reciprocal L5A to L2/3 connection. This pathway may be homologous to the prominent
L4/5A to L2/3 pathway in sensory cortex. Also – as in sensory cortex – recurrent
(intralaminar) connections were prominent, particularly in L2, L5A/B and L6. The largest
fraction of synaptic input arrived in L5A/B, consistent with its key role in accumulating
information from a wide range of afferents – before sending its output to the corticospinal
tract. In summary, strong input-layer to superficial, and superficial to deep connectivity,
together with strong intralaminar connectivity, suggests that the intrinsic circuitry of motor
cortex is similar to other cortical areas.

The anatomy and physiology of extrinsic connections

Clearly, an account of microcircuits must refer to the layers of origin of extrinsic
connections and their laminar targets. Although the majority of presynaptic inputs arise from
intrinsic connections, cortical areas are also richly interconnected, where the balance
between intrinsic and extrinsic processing mediates functional integration among specialised
cortical areas (Engel et al., 2010). By numbers alone, intrinsic connections appear to
dominate – 95% of all neurons labelled with a retrograde tracer lie within about 2 mm of the
injection site (Markov et al., 2011). The remaining 5% represent cells giving rise to extrinsic
connections, which – although sparse – can be extremely effective in driving their targets. A
case in point is the LGN to V1 connection: although it is only the sixth strongest connection
to V1, LGN afferents have a substantial effect on V1 responses (Markov et al., 2011).

Hierarchies and functional asymmetries—Current dogma holds that the cortex is
hierarchically organized. The idea of a cortical hierarchy rests on the distinction between
three types of extrinsic connections: feedforward connections, that link an earlier area to a
higher area, feedback connections, that link a higher to an earlier area, and lateral
connections, that link areas at the same level (reviewed in Felleman and Van Essen, 1991).
These connections are distinguished by their laminar origins and targets. Feedforward
connections originate largely from superficial pyramidal cells and target L4, while feedback
connections originate largely from deep pyramidal cells and terminate outside of L4
(Felleman and van Essen 1991). Clearly, this description of cortical hierarchies is a
simplification and can be nuanced in many ways: for example, as the hierarchical distance
between two areas increases, the percentage of cells that send feedforward (resp. feedback)
projections from a lower (resp. higher) level becomes increasingly biased towards the
superficial (resp. deep) layers (Barone et al., 2000; Vezoli, 2004) .

In addition to the laminar specificity of their origins and targets, feedforward and feedback
connections also differ in their synaptic physiology. The traditional view holds that
feedforward connections are strong and driving, capable of eliciting spiking activity in their
targets and conferring classical receptive field properties – the prototypical example being
the synaptic connection between LGN and V1 (Sherman and Guillery, 1998). Feedback
connections are thought to modulate (extra-classical) receptive field characteristics
according to the current context; e.g., visual occlusion, attention, salience, etc. The
prototypical example of a feedback connection is the cortical L6 to LGN connection.
Sherman and Guillery identified several properties that distinguish drivers from modulators.
Driving connections tend to show a strong ionotropic component in their synaptic response,
evoke large EPSPs, and respond to multiple EPSPs with depressing synaptic effects.
Modulatory connections produce metabotropic and ionotropic responses when stimulated,
evoke weak EPSPs, and show paired-pulse facilitation (Sherman and Guillery, 1998; 2011).

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These distinctions were based upon the inputs to the LGN, where retinal input is driving and
cortical input is modulatory. Until recently, little data were available to assess whether a
similar distinction applies to cortico-cortical feedforward and feedback connections.
However, recent studies show that cortical feedback connections express not only
modulatory but also driving characteristics:

Are feedback connections driving, modulatory or both?—Although it is generally
thought that feedback connections are weak and modulatory (Crick and Koch, 1998;
Sherman and Guillery, 1998), recent evidence suggests that feedback connections do more
than modulate lower level responses: Sherman and colleagues recorded cells in mouse area
V1/V2 and A1/A2, while stimulating feedforward or feedback afferents. In both cases,
driving-like responses as well as modulatory-like responses were observed (Covic and
Sherman, 2011; De Pasquale and Sherman, 2011). This indicates that – for these
hierarchically proximate areas – feedback connections can drive their targets just as strongly
as feedforward connections. This is consistent with earlier studies showing that feedback
connections can be driving: Mignard and Malpeli (1991) studied the feedback connection
between areas 18 and 17, while layer A of the LGN was pharmacologically inactivated. This
silenced the cells in L4 in area 17 but spared activity in superficial layers. However,
superficial cells were silenced when area 18 was lesioned. This is consistent with a driving
effect of feedback connections from area 18, in the absence of geniculate input. In summary,
feedback connections can mediate modulatory and driving effects. This is important from
the point of view of predictive coding, because top-down predictions have to elicit
obligatory responses in their targets (cells reporting prediction errors):

In predictive coding, feedforward connections convey prediction errors, while feedback
connections convey predictions from higher cortical areas to suppress prediction errors in
lower areas. In this scheme, feedback connections should therefore be capable of exerting
strong (driving) influences on earlier areas to suppress or counter feedforward driving
inputs. However, as we will see later, these influences also need to exert nonlinear or
modulatory effects. This is because top-down predictions are necessarily context sensitive:
e.g., the occlusion of one visual object by another. In short, predictive coding requires
feedback connections to drive cells in lower levels in a context sensitive fashion, which
necessitates a modulatory aspect to their postsynaptic effects.

Are feedback connections excitatory or inhibitory?—Crucially, because feedback
connections convey predictions – that serve to explain and thereby reduce prediction errors
in lower levels – their effective (polysynaptic) connectivity is generally assumed to be
inhibitory. An overall inhibitory effect of feedback connections is consistent with in vivo
studies. For example, electrophysiological studies of the mismatch negativity suggest that
neural responses to deviant stimuli – that violate sensory predictions established by a regular
stimulus sequence – are enhanced relative to predicted stimuli (Garrido et al., 2009).
Similarly, violating expectations of auditory repetition causes enhanced gamma-band
responses in early auditory cortex (Todorovic et al., 2011). These enhanced responses are
thought to reflect an inability of higher cortical areas to predict, and thereby suppress, the
activity of populations encoding prediction error (Garrido et al., 2007; Wacongne et al.,
2011). The suppression of predictable responses can also be regarded as repetition
suppression, observed in single unit recordings from the inferior temporal cortex of macaque
monkeys (Desimone, 1996). Furthermore, neurons in monkey inferotemporal cortex respond
significantly less to a predicted sequence of natural images, compared to an unpredicted
sequence (Meyer and Olson, 2011).

The inhibitory effect of feedback connections is further supported by neuroimaging studies
(Murray et al., 2002; Murray, 2005; Harrison et al., 2007; Summerfield et al., 2008, 2011;

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Alink et al., 2010). These studies show that predictable stimuli evoke smaller responses in
early cortical areas. Crucially, this suppression cannot be explained in terms of local
adaptation, because the attributes of the stimuli that can be predicted are not represented in
early sensory cortex (e.g., Harrison et al. 2007). It should be noted that the suppression of
responses to predictable stimuli can coexist with (top-down) attentional enhancement of
signal processing (Wyart et al., 2012): in predictive coding, attention is mediated by
increasing the gain of populations encoding prediction error (Spratling, 2008; Feldman and
Friston, 2010). The resulting attentional modulation (e.g., Hopfinger et al., 2000) can
interact with top-down predictions to override their suppressive influence – as demonstrated
empirically (Kok et al., 2011). See Buschman and Miller, (2007), Saalmann et al., (2007),
Anderson et al. (2011), and Armstrong et al. (2012) for further discussion of top-down
connections in attention.

Further evidence for the inhibitory (suppressive) effect of feedback connections comes from
neuropsychology: Patients with damage to the prefrontal cortex (PFC) show disinhibition of
event related potential responses (ERP) to repeating stimuli (Knight et al., 1989; Yamaguchi
and Knight, 1990; but see Barceló et al., 2000). In contrast, they show reduced-amplitude
P300 ERPs in response to novel stimuli – as if there were a failure to communicate top-
down predictions to sensory cortex (Knight, 1984). Furthermore, normal subjects show a
rapid adaptation to deviant stimuli as they become predictable – an effect not seen in
prefrontal patients.

Several invasive studies complement these human studies in suggesting an overall inhibitory
role for feedback connections. In a recent seminal study, Olsen et al. studied corticothalamic
feedback between L6 of V1 and the LGN using transgenic expression of channel rhodopsin
in L6 cells of V1. By driving these cells optogenetically – while recording units in V1 and
the LGN – the authors showed that deep L6 principal cells inhibited their extrinsic targets in
the LGN and their intrinsic targets in cortical layers 2 to 5 (Olsen et al., 2012). This
suppression was powerful – in the LGN, visual responses were suppressed by 76%.
Suppression was also high in V1, around 80-84% (Olsen et al., 2012). This evidence is in
line with classical studies of corticogeniculate contributions to length tuning in the LGN,
showing that cortical feedback contributes to the surround suppression of feline LGN cells:
without feedback, LGN cells are disinhibited and show weaker surround suppression
(Murphy and Sillito, 1987; Sillito et al., 1993; but see Alitto and Usrey, 2008).

While these studies provide convincing evidence that cortical feedback to the LGN is
inhibitory, the evidence is more complicated for corticocortical feedback connections
(Sandell and Schiller, 1982; Johnson and Burkhalter, 1996, 1997). Hupé and colleagues
cooled area V5/MT while recording from areas V1, V2, and V3 in the monkey. When visual
stimuli were presented in the classical receptive field (CRF), cooling of area V5/MT
decreased unit activity in earlier areas, suggesting an excitatory effect of extrinsic feedback
(Hupé et al., 1998). However, when the authors used a stimulus that spanned the extra-
classical RF the responses of V1 neurons were – on average – enhanced after cooling area
V5, consistent with the suppressive role of feedback connections. These results indicate that
the inhibitory effects of feedback connections may depend on (natural) stimuli that require
integration over the visual field. Similar effects were observed when area V2 was cooled and
neurons were measured in V1: when stimuli were presented only to the CRF, cooling V2
decreased V1 spiking activity; however, when stimuli were present in the CRF and the
surround, cooling V2 increased V1 activity (Bullier et al., 1996). Finally, others have argued
for an inhibitory effect of feedback based on the timing and spatial extent of surround
suppression in monkey V1 – concluding that the far surround suppression effects were most
likely mediated by feedback (Bair et al., 2003).

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The empirical finding that feedback connections can both facilitate and suppress firing in
lower hierarchical areas – depending on the content of classical and extra-classical receptive
fields – is consistent with predictive coding: Rao and Ballard (1999) trained a hierarchical
predictive coding network to recognise natural images. They showed that higher levels in
the hierarchy learn to predict visual features that extend across many CRFs in the lower
levels (e.g. tree trunks or horizons). Hence, higher visual areas come to predict that visual
stimuli will span the receptive fields of cells in lower visual areas. In this setting, a stimulus
that is confined to a CRF would elicit a strong prediction error signal (because it cannot be
predicted). This provides a simple explanation for the findings of Hupé et al (1998) and
Bullier et al (1996): when feedback connections are deactivated, there are no top-down
predictions to explain responses in lower areas – leading to a disinhibition of responses in
earlier areas, when – and only when – stimuli can be predicted over multiple CRFs.

Feedback connections and layer 1—How might the inhibitory effect of feedback
connections be mediated? The established view is that extrinsic corticocortical connections
are exclusively excitatory (using glutamate as their excitatory neurotransmitter) – although
recent evidence suggests that inhibitory extrinsic connections exist and may play an
important role in synchronizing distant regions (Melzer et al., 2012). However, one
important route by which feedback connections could mediate selective inhibition is via
their termination in L1 (Anderson and Martin, 2006; Shipp, 2007): layer 1 is sometimes
referred to as acellular due to its pale appearance with Nissl staining (the classical method
for separating layers that selectively labels cell bodies). Indeed, a recent study concluded
that L1 contains less than 0.5% of all cells in a cortical column (Meyer et al., 2011). These
L1 cells are almost all inhibitory and interconnect strongly with each other, via electrical
connections and chemical synapses (Chu et al., 2003). Simultaneous whole cell patch clamp
recordings show that they provide strong monosynaptic inhibition to L2/3 pyramidal cells,
whose apical dendrites project into L1 (Chu et al., 2003; Wozny and Williams, 2011). This
means L1 inhibitory cells are in a prime position to mediate inhibitory effects of extrinsic
feedback. The laminar location highlighted by these studies – the bottom of L1 and the top
of L2/3 – has recently been shown to be a “hotspot” of inhibition in the column (Meyer et
al., 2011). Indeed, a study of rat barrel cortex – that stimulated (and inactivated) L1 –
showed that it exerts a powerful inhibitory effect on whisker-evoked responses (Shlosberg et
al., 2006). These studies suggest that corticocortical feedback connections could deliver
strong inhibition, if they were to recruit the inhibitory potential of L1.

In terms of the excitatory and modulatory effect of feedback connections, predictive input
from higher cortical areas might have an important impact via the distal dendrites of
pyramidal neurons (Larkum et al., 2009). Furthermore, there is a specific type of
GABAergic neuron that appears to control distal dendritic excitability, gating top down
excitatory signals differentially during behavior (Gentet et al., 2012). Table 1 summarises
the studies we have discussed in relation to the role of feedback connections.

Feedforward and transthalamic connections

While the evidence for an inhibitory effect of feedback connections has to be evaluated
carefully, the evidence for an excitatory effect of feedforward connections is unequivocal.
For example, in the monkey, V1 projects monosynaptically to V2, V3, V3a, V4, and V5/MT
(Zeki, 1978; Zeki and Shipp, 1988). In all cases – when V1 is reversibly inactivated through
cooling – single-cell activity in target areas is strongly suppressed (Girard and Bullier, 1989;
Girard et al., 1991a, 1991b, 1992). In the cases of V2 and V3, the result of cooling area V1
is a near-total silencing of single unit activity. These studies illustrate that activity in higher
cortical areas depends on driving inputs from earlier cortical areas that establish their
receptive field properties.

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Finally, while many studies have focused on extrinsic connections that project directly from
one cortical area to the next, there is mounting evidence that feedforward driving
connections (and perhaps feedback) in the cortex could be mediated by transthalamic
pathways (Sherman and Guillery, 1998, 2011). The strongest evidence for this claim comes
from the somatosensory system, where it was shown recently that the posterior medial
nucleus of the thalamus (POm) – a higher-order thalamic nucleus that receives direct input
from cortex – can relay information between S1 and S2 (Theyel et al., 2009). In addition, the
thalamic reticular nucleus has been proposed to mediate the inhibition that might underlie
cross-modal attention or top-down predictions (Yamaguchi and Knight, 1990; Crick, 1984;
Wurtz et al., 2011). Furthermore, computational considerations and recent experimental
findings point to a potentially important role for higher-order thalamic nuclei in coordinating
and synchronizing cortical responses (Vicente et al., 2008; Saalmann et al., 2012). The
degree to which cortical areas are integrated directly via corticocortical or indirectly via
cortico-thalamo-cortical connections – and the extent to which transthalamic pathways
dissociate feedforward from feedback connections in the same way as we have proposed for
the cortico-cortical connections – are open questions.

The canonical microcircuit

Central to the idea of a canonical microcircuit is the notion that a cortical column contains
the circuitry necessary to perform requisite computations, and that these circuits can be
replicated with minor variations throughout the cortex. One of the clearest examples of how
cortical circuits process simple inputs – to generate complex outputs – is the emergence of
orientation tuning in V1. Orientation tuning is a distinctly cortical phenomenon because
geniculocortical relay cells show no orientation preferences. A further elaboration of cortical
responses can be found in the distinction between simple and complex cells – while simple
cells possess spatially confined receptive fields, complex cells are orientation-tuned but
show less preference for the location of an oriented bar. Hubel and Wiesel proposed a model
for how intrinsic and extrinsic connectivity could establish a circuit explaining these
receptive field properties. They proposed that orientation tuning in simple cells could be
generated by a single cortical cell receiving input from several ON centre – OFF surround
geniculate cells arranged along a particular orientation, thereby endowing it with a
preference for bars oriented in a particular direction (Hubel and Wiesel, 1962). Complex
cells were hypothesized to receive inputs from several simple cells – with the same
orientation preference and slightly varying receptive field locations. Thus, complex cells
were thought not to receive direct LGN input but to be higher order cells in cortex.
Subsequent findings supported these predictions, showing that input layer 4Cα and 4Cβ
contained the largest proportion of cells receiving monosynaptic geniculate input, while
superficial and deep layer cells contain a larger number of cells receiving disynaptic or
polysynaptic input (Bullier and Henry, 1980). Furthermore, simple cells project
monosynaptically onto complex cells, where they exert a strong feedforward influence
(Alonso and Martinez, 1998; Alonso, 2002). These models suggest that intrinsic cortical
circuitry allows processing to proceed along discrete steps that are capable of producing
response properties in outputs that are not present in inputs.

Segregation of processing streams

A key property of canonical circuits is the segregation of parallel streams of processing. For
example, in primates, parvocellular input enters the cortex primarily in layer 4Cβ, whereas
magnocellular inputs enter in 4Cα. The corticogeniculate feedback pathway from L6
maintains this segregation, as upper L6 cells preferentially synapse onto parvocellular cells
in the LGN, while lower L6 cells target the magnocellular LGN layers (Fitzpatrick et al.,
1994; Briggs and Usrey, 2009). Further examples of stream segregation are also present in

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the dorsal “where” and the ventral “what” pathways, and in the projection from V1 to the
thick, thin, and inter-stripe regions of V2 (Zeki and Shipp, 1988; Sincich and Horton, 2005).

Superficial and deep layers are anatomically interconnected, but mounting evidence suggests
that they constitute functionally distinct processing streams: in an elegant experiment,
Roopun et al. (2006) showed that L2/3 of rat somatomotor cortex shows prominent gamma
oscillations that are co-expressed with beta oscillations in L5. Both rhythms persisted, when
superficial and deep layers were disconnected at the level of L4. Maier and colleagues
(2010) used multilaminar recordings to show strong LFP coherence amongst sites within the
superficial layers (the superficial compartment), as well as strong coherence amongst sites in
deep layers (the deep compartment), but weak inter-compartment coherence. These studies
indicate a segregation of – potentially autonomous – supragranular and infragranular
dynamics. Maier et al., found that supragranular sites had higher broadband gamma power
than infragranular sites. This pattern was reversed in the alpha and beta range; with greater
power in the infragranular and granular layers. Finally, the spiking activity of neurons in the
superficial layers of visual cortex are more coherent with gamma frequency oscillations in
the local field potential, while neurons in deep layers are more coherent with alpha
frequency oscillations (Buffalo et al., 2011). This finding is consistent with an earlier study
by Livingstone (1996) showing that 50% of cells in L2/3 of squirrel monkey V1 expressed
gamma oscillations, compared to less than 20% of cells in L4C and infragranular layers. The
different spectral behaviour of superficial and deep layers has led to the interesting proposal
that feedforward and feedback signalling may be mediated by distinct (high and low)
frequencies (reviewed in Wang, 2010, see also Buschman and Miller, 2007 in the context of
attention), a proposal that has recently received experimental support - at least for the
feedforward connections (Bosman et al., 2012; see also Gregoriou et al., 2009).

Integration and segregation within canonical circuits—Given this functional and
anatomical segregation into parallel streams, the question naturally arises, how are these
streams integrated? It has been previously suggested that integration occurs through the
synchronized firing of multiple neurons that form a neural ensemble (Gray et al., 1989;
Singer, 1999), while others have emphasized inter-areal phase-synchronization or coherence
(Varela et al., 2001; Fries, 2005; Fujisawa and Buzsáki, 2011). While a full treatment of this
question is beyond the scope of the current review, we propose that the canonical
microcircuit contains a clue for how the dialectic between segregation and integration might
be resolved. While top-down and bottom-up inputs and outputs may be segregated in layers,
streams, and frequency bands, the canonical microcircuit specifies the circuitry for how the
basic units of cortex are interconnected and therefore how the intrinsic activity of the
cortical column is entrained by extrinsic inputs. This intrinsic connectivity specifies how the
cells of origin and termination of extrinsic projections are interconnected, and thus
determine how top-down and bottom-up streams are integrated within each cortical column.

Spatial segregation and cortical columns

The notion of a canonical microcircuit implicitly assumes that each circuit is distinct from
its neighbours; that could presumably carry out computations in parallel. Therefore, the
canonical microcircuit specifies the spatial scale over which processing is integrated. The
most likely candidate for this spatial scale is the cortical column – that can vary over three
orders of magnitude between minicolumns, columns, and hypercolumns. Minicolumns are
only a few cells wide, estimated to be about 50-60 micrometers in diameter by Mountcastle
(1997) and are seen in Nissl sections of cortex as slight variations in cell density.
Minicolumns were originally proposed as elementary units of cortex by Lorente de No
(1949) and appear to reflect the migration of cells from the ventricular zone to the cortical
sheet during foetal development (reviewed in Horton and Adams, 2005). Hubel and Wiesel

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estimated that orientation columns were on this order of magnitude, about 25-50
micrometers wide, although they failed to establish a correspondence between orientation
columns observed physiologically and the minicolumns seen in Nissl sections (Hubel and
Wiesel, 1974). A cortical column was classically defined as a vertical alignment of cells
containing neurons with similar receptive field properties, such as orientation preference and
ocular dominance in V1; or touch in somatosensory cortex (Mountcastle, 1957; Hubel and
Wiesel, 1972). These columns were suggested by Mountcastle to encompass a number of
minicolumns, with a width of 300-400 micrometers (Mountcastle, 1997). Finally, Hubel and
Wiesel defined a hypercolumn to be the unit of cortex necessary to traverse all possible
values of a particular receptive field property, such as orientation or eye dominance –
estimated to be between 0.5 to 1 mm wide (Hubel and Wiesel, 1974).

Columns, connections and computations—So is the cortical column the basic unit
of cortical computation? Some authors emphasize that even within a dendrite, there are all
the necessary biophysical mechanisms for performing surprisingly advanced computations,
such as direction selectivity, coincidence detection, or temporal integration (Häusser and
Mel, 2003; London and Häusser, 2005). Others argue that single neurons can process their
inputs at the dendrite, soma, and initial segment, such that the output spike trains of just two
interconnected cells could mediate computations like independent components analysis
(Klampfl et al., 2009). Others posit that cortical columns form the basic computational unit
(Mountcastle, 1997; Hubel and Wiesel, 1972) but see (Horton and Adams, 2005). Donald
Hebb proposed that neurons distributed over several cortical areas could form a functional
computational unit called a neural assembly (Hebb, 1949). This view has re-emerged in
recent years, with the development of the requisite recording and analytic techniques for
evaluating this proposal (Buzsáki, 2010; Canolty et al., 2010; Singer et al., 1997; Lopes-dos-
Santos et al., 2011).

Computational modelling studies indicate that cortical columns with structured connectivity
are computationally more efficient than a network containing the same number of neurons
but with random connectivity (Haeusler and Maass, 2007). Others suggest that this circuitry
allows the cortex to organize and integrate bottom-up, lateral, and top-down information
(Ullman, 1995; Raizada and Grossberg, 2003). Douglas and Martin suggest that the rich
anatomical connectivity of L2/3 pyramidal cells allows them to collect information from
top-down, lateral, and bottom-up inputs, and – through processing in the dendritic tree –
select the most likely interpretation of its inputs. More recently, George and Hawkins have
suggested that the canonical microcircuit implements a form of Bayesian processing
(George and Hawkins, 2009). In the following section, we pursue similar ideas, but ground
them in the framework of predictive coding, and propose a cortical circuit that could
implement predictive coding through canonical interconnections. In particular, we find that
the proposed circuitry agrees remarkably well with quantitative characterisations of the
canonical microcircuit (Haeusler and Maass, 2007).

A canonical microcircuit for predictive coding

This section considers the computational role of cortical microcircuitry in more detail. We
try to show that the computations performed by canonical microcircuits can be specified
more precisely than one might imagine and that these computations can be understood
within the framework of predictive coding. In brief, we will show that (hierarchical
Bayesian) inference about the causes of sensory input can be cast as predictive coding. This
is important because it provides formal constraints on the dynamics one would expect to
find in neuronal circuits. Having established these constraints, we then attempt to match
them with the neurobiological constraints afforded by the canonical microcircuit. The
endpoint of this exercise is a canonical microcircuit for predictive coding.

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Predictive coding and the free energy principle

It might be thought impossible to specify the computations performed by the brain.
However, there are some fairly fundamental constraints on the basic form of neuronal
dynamics. The argument goes as follows – and can be regarded as a brief summary of the
free energy principle (see Friston, 2010 for details):

•
Biological systems are homoeostatic (or allostatic), which means that they
minimise the dispersion (entropy) of their interoceptive and exteroceptive states.

•
Entropy is the average of surprise over time, which means biological systems
minimise the surprise associated with their sensory states at each point in time.

•
In statistics, surprise is the negative logarithm of Bayesian model evidence, which
means biological systems – like the brain – must continually maximise the
Bayesian evidence for their (generative) model of sensory inputs.

•
Maximising Bayesian model evidence corresponds to Bayesian filtering of sensory
inputs. This is also known as predictive coding.

These arguments mean that by minimising surprise, through selecting appropriate
sensations, the brain is implicitly maximising the evidence for its own existence – this is
known as active inference. In other words, to maintain a homoeostasis the brain must predict
its sensory states on the basis of a model. Fulfilling those predictions corresponds to
accumulating evidence for that model – and the brain that embodies it. The implicit
maximisation of Bayesian model evidence provides an important link to the Bayesian brain
hypothesis (Hinton and van Camp, 1993; Dayan et al., 1995; Knill and Pouget, 2004) and
many other compelling proposals about perceptual synthesis – including analysis by
synthesis (Neisser, 1967; Yuille and Kersten, 2006) epistemological automata (MacKay,
1956), the principle of minimum redundancy (Attneave, 1954; Barlow, H.B., 1961; Dan et
al., 1996), the Infomax principle (Linsker, 1990; Atick, 1992; Kay and Phillips, 2011), and
perception as hypothesis testing (Gregory, 1968; 1980).

The most popular scheme – for Bayesian filtering in neuronal circuits – is predictive coding
(Srinivasan et al., 1982; Buchsbaum and Gottschalk, 1983; Rao and Ballard, 1999). In this
context, surprise corresponds (roughly) to prediction error. In predictive coding, top-down
predictions are compared with bottom-up sensory information to form a prediction error.
This prediction error is used to update higher-level representations – upon which top-down
predictions are based. These optimised predictions then reduce prediction error at lower
levels.

To predict sensations, the brain must be equipped with a generative model of how its
sensations are caused (Helmholtz, 1860). Indeed, this led Geoffrey Hinton and colleagues to
propose that the brain is an inference (Helmholtz) machine (Hinton and Zemel, 1994; Dayan
et al., 1995). A generative model describes how variables or causes in the environment
conspire to produce sensory input. Generative models map from (hidden) causes to (sensory)
consequences. Perception then corresponds to the inverse mapping from sensations to their
causes, while action can be thought of as the selective sampling of sensations. Crucially, the
form of the generative model dictates the form of the inversion – for example, predictive
coding. Figure 3 depicts a general model as a probabilistic graphical model. A special case
of these models are hierarchical dynamic models (see Figure 4), which grandfather most
parametric models in statistics and machine learning (see Friston, 2008). These models
explain sensory data in terms of hidden causes and states. Hidden causes and states are both
hidden variables that cause sensations but they play slightly different roles: hidden causes
link different levels of the model and mediate conditional dependencies among hidden states
at each level. Conversely, hidden states model conditional dependencies over time (i.e.,

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memory) by modelling dynamics in the world. In short, hidden causes and states mediate
structural and dynamic dependencies respectively.

The details of the graph in Figure 3 are not important; it just provides a way of describing
conditional dependencies among hidden states and causes responsible for generating sensory
input. These dependencies mean that we can interpret neuronal activity as message passing
among the nodes of a generative model, where each canonical microcircuit contains
representations or expectations about hidden states and causes. In other words, the form of
the underlying generative model defines the form of the predictive coding architecture used
to invert the model. This is illustrated in Figure 4, where each node has a single parent. We
will deal with this simple sort of model because it lends itself to an unambiguous description
in terms of bottom-up (feedforward) and top-down (feedback) message passing. We now
look at how perception or model inversion – recovering the hidden states and causes of this
model given sensory data – might be implemented at the level of a microcircuit:

Predictive coding and message passing

In predictive coding, representations (or conditional expectations) generate top-down
predictions to produce prediction errors. These prediction errors are then passed up the
hierarchy in the reverse direction, to update conditional expectations. This ensures an
accurate prediction of sensory input and all its intermediate representations. This hierarchal
message passing can be expressed mathematically as a gradient descent on the (sum of
squared) prediction errors 
, where the prediction errors are weighted by their
precision (inverse variance).

(1)

The first pair of equalities just says that conditional expectations about hidden causes and

states 
 are updated based upon the way we would predict them to change – the first
term – and subsequent terms that minimise prediction error. The second pair of equations

simply expresses prediction error 
 as the difference between conditional
expectations about hidden causes and (the changes in) hidden states and their predicted

values, weighed by their precisions 
. These predictions are nonlinear functions of
conditional expectations (g(i), f(i)) at each level of the hierarchy and the level above.

It is difficult to overstate the generality and importance of Equation (1) – it grandfathers
nearly every known statistical estimation scheme, under parametric assumptions about
additive noise. These range from ordinary least squares to advanced Bayesian filtering
schemes (see Friston 2008). In this general setting, Equation (1) minimises variational free
energy and corresponds to generalised predictive coding. Under linear models, it reduces to
linear predictive coding, also known as Kalman-Bucy filtering (see Friston et al, 2010 for
details).

In neuronal network terms, Equation (1) says that prediction error units receive messages
from the same level and the level above. This is because the hierarchical form of the model
only requires conditional expectations from neighbouring levels to form prediction errors, as
can be seen schematically in Figure 4. Conversely, expectations are driven by prediction

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error from the same level and the level below – updating expectations about hidden states
and causes respectively. These constitute the bottom-up and lateral messages that drive
conditional expectations to provide better predictions – or representations – that suppress
prediction error. This updating corresponds to an accumulation of prediction errors – in that
the rate of change of conditional expectations is proportional to prediction error.
Electrophysiologically, this means that one would expect to see a transient prediction error
response to bottom-up afferents (in neuronal populations encoding prediction error) that is
suppressed to baseline firing rates by sustained responses (in neuronal populations encoding
predictions). This is the essence of recurrent message passing between hierarchical levels to
suppress prediction error (see Friston 2008 for a more detailed discussion).

The nature of this message passing is remarkably consistent with the anatomical and
physiological features of cortical hierarchies. An important prediction is that the nonlinear
functions of the generative model – modelling context sensitive dependencies among hidden
variables – appear only in the top-down and lateral predictions. This means,
neurobiologically, we would predict feedback connections to possess nonlinear or
neuromodulatory characteristics; in contrast to feedforward connections that mediate a linear
mixture of prediction errors. This functional asymmetry is exactly consistent with the
empirical evidence reviewed above. Another key feature of Equation (1) is that the top-
down predictions produce prediction errors through subtraction. In other words, feedback
connections should exert inhibitory effects, of the sort seen empirically. Table 2 summarises
the features of extrinsic connectivity (reviewed in the previous section) that are explained by
predictive coding. In the remainder of this review, we focus on intrinsic connections and
cortical microcircuits.

The cortical microcircuit and predictive coding

We now try to associate the variables in Equation (1) with specific populations in the
canonical microcircuit. Figure 5 illustrates a remarkable correspondence between the form
of Equation (1) and the connectivity of the canonical microcircuit. Furthermore, the
resulting scheme corresponds almost exactly to the computational architecture proposed by
Mumford (1992). This correspondence rests upon the following intuitive steps:

•
First, we divide the excitatory cells in the superficial and deep layers into principal
(pyramidal) cells and excitatory interneurons. This accommodates the fact that (in
macaque V1) a significant percentage of superficial L2/3 cells (about half) and
deep L5 excitatory cells (about 80%) do not project outside the cortical column
(Callaway and Wiser, 1996; Briggs and Callaway, 2005).

•
Second, we know that the superficial and deep pyramidal cells provide feedforward
and feedback connections respectively. This means that superficial pyramidal cells

must encode and broadcast prediction errors on hidden causes 
, while deep

pyramidal cells must encode conditional expectations 
 so that they can
elaborate feedback predictions.

•
Third, we know that the (spiny stellate) excitatory cells in the granular layer receive

feedforward connections encoding prediction errors 
 on the hidden causes of the
level below.

•
This leaves the inhibitory interneurons in the granular layer, which, for symmetry,
we associate with prediction errors on the hidden states.

•
The remaining populations are the excitatory and inhibitory interneurons in the
supragranular layer, to which we assign expectations about hidden causes and
states respectively. These are mapped through descending (intrinsic) feedforward

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connections to cells in the deep layers that generate predictions. We do not suppose
that this is a simple one-to-one mapping – rather it mediates the nonlinear
transformation of expectations to predictions required by the earlier cortical level.

This arrangement accommodates the fact that the dependencies among hidden states are
confined to each node (by the nature of graphical models), which means that their
expectations and prediction errors should be encoded by interneurons. Furthermore, the
splitting of excitatory cells in the upper layers into two populations (encoding expectations
and prediction errors on hidden causes) is sensible, because there is a one-to-one mapping
between the expectations on hidden causes and their prediction errors.

The ensuing architecture bears a striking correspondence to the microcircuit in (Haeusler
and Maass, 2007) in the left panel of Figure 5 – in the sense that nearly every connection
required by the predictive coding scheme appears to be present in terms of quantitative
measures of intrinsic connectivity. However, there are two exceptions that both involve
connections to the inhibitory cells in the granular layer (shown as dotted lines in Figure 5).
Predictive coding requires that these cells (that encode prediction errors on hidden states)
compare the expected changes in hidden states with the actual changes. This suggests that
there should be interlaminar projections from supragranular (inhibitory) and infragranular
(excitatory) cells. In terms of their synaptic characteristics, one would predict that these
intrinsic connections would be of a feedback sort – in the sense that they convey predictions.
Although not considered in this Haeusler and Maass scheme, feedback connections from
infragranular layers are an established component of the canonical microcircuit (see Figure
2).

Functional asymmetries in the microcircuit

The circuitry in Figure 5 appears consistent with the broad scheme of ascending
(feedforward) and descending (feedback) intrinsic connections: feedforward prediction
errors from a lower cortical level arrive at granular layers and are passed forward to
excitatory and inhibitory interneurons in supragranular layers, encoding expectations. Strong
and reciprocal intralaminar connections couple superficial excitatory interneurons and
pyramidal cells. Excitatory and inhibitory interneurons in supragranular layers then send
strong feedforward connections to the infragranular layer. These connections enable deep
pyramidal cells and excitatory interneurons to produce (feedback) predictions, which ascend
back to L4 or descend to a lower hierarchical level. This arrangement recapitulates the
functional asymmetries between extrinsic feedforward and feedback connections and is
consistent with the empirical characteristics of intrinsic connections.

If we focus on the superficial and deep pyramidal cells, the form of the recognition
dynamics in Equation (1) tells us something quite fundamental: We would anticipate higher
frequencies in the superficial pyramidal cells, relative to the deep pyramidal cells. One can
see this easily by taking the Fourier transform of the first equality in Equation (1)

(2)

This equation says that the contribution of any (angular) frequency ω in the prediction errors
(encoded by superficial pyramidal cells) to the expectations (encoded by the deep pyramidal
cells) is suppressed in proportion to that frequency (Friston 2008). In other words, high
frequencies should be attenuated when passing from superficial to deep pyramidal cells.
There is nothing mysterious about this attenuation – it is a simple consequence of the fact
that conditional expectations accumulate prediction errors, thereby suppressing high-
frequency fluctuations to produce smooth estimates of hidden causes. This smoothing –

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inherent in Bayesian filtering – leads to an asymmetry in frequency content of superficial
and deep cells: for example, superficial cells should express more gamma relative to beta,
and deep cells should express more beta relative to gamma (Roopun et al., 2006, 2008;
Maier et al., 2010).

Figure 6 provides a schematic illustration of the spectral asymmetry predicted by Equation
2. Note that predictions about the relative amplitudes of high and low frequencies in
superficial and deep layers pertain to all frequencies – there is nothing in predictive coding
per se to suggest characteristic frequencies in the gamma and beta ranges. However, one
might speculate the characteristic frequencies of canonical microcircuits have evolved to
model and – through active inference – create the sensorium (Friston, 2010; Berkes et al.,
2011; Engbert et al., 2011). Indeed, there is empirical evidence to support this notion; in the
visual (Lakatos et al., 2008; Meirovithz et al., 2012; Bosman et al., 2009) and motor domain
(Gwin and Ferris, 2012).

In summary, predictions are formed by a linear accumulation of prediction errors.
Conversely, prediction errors are nonlinear functions of predictions. This means that the
conversion of prediction errors into predictions (Bayesian filtering) necessarily entails a loss
of high frequencies. However, the nonlinearity in the mapping from predictions to prediction
errors means that high frequencies can be created (consider the effect of squaring a sine
wave, which would convert beta into gamma). In short, prediction errors should express
higher frequencies than the predictions that accumulate them. This is another example of a
potentially important functional asymmetry between feedforward and feedback message
passing that emerges under predictive coding. It is particularly interesting given recent
evidence that feedforward connections may use higher frequencies than feedback
connections (Bosman et al., 2012).

Conclusion

In conclusion, there is a remarkable correspondence between the anatomy and physiology of
the canonical microcircuit and the formal constraints implied by generalised predictive
coding. Having said this, there are many variations on the mapping between computational
and neuronal architectures: Even if predictive coding is an appropriate implementation of
Bayesian filtering, there are many variations on the arrangement shown in Figure 5. For
example, feedback connections could arise directly from cells encoding conditional
expectations in supragranular layers. Indeed, there is emerging evidence that feedback
connections between proximate hierarchical levels originate from both deep and superficial
layers (Markov et al 2011). Note that this putative splitting of extrinsic streams is only
predicted in the light of empirical constraints on intrinsic connectivity.

One of our motivations – for considering formal constraints on connectivity – was to
produce dynamic causal models of canonical microcircuits. Dynamic causal modelling
enables one to compare different connectivity models, using empirical electrophysiological
responses (David et al, 2006; Moran et al, 2008, 2011). This form of modelling rests upon
Bayesian model comparison and allows one to assess the evidence for one microcircuit
relative to another. In principle, this provides a way to evaluate different microcircuit
models, in terms of their ability to explain observed activity. One might imagine that the
particular circuits for predictive coding presented in this paper will be nuanced as more
anatomical and physiological information becomes available. The ability to compare
competing models or microcircuits – using optogenetics, local field potentials and
electroencephalography – may be important for refining neurobiologically informed
microcircuits. In short, many of the predictions and assumptions we have made about the
specific form of the microcircuit for predictive coding may be testable in the near future.

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Acknowledgments

This work was supported by the Wellcome Trust and the NSF Graduate Research Fellowship under Grant No.
2009090358 to A.M.B. Support was also provided by NIH grants MH055714 (G.R.M.) and EY013588 (W.M.U.),
and NSF grant 1228535 (G.R.M and W.M.U). The authors would like to thank Julien Vezoli, Will Penny, Dimitris
Pinotsis, Stewart Shipp, Vladimir Litvak, Conrado Bosman, Laurent Perrinet and Henry Kennedy for helpful
discussions. We would also like to thank our reviewers for helpful comments and guidance.

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Figure 1.
This is a schematic of the classical microcircuit adapted from Douglas and Martin (1991).
This minimal circuitry comprises superficial (layers 2 and 3) and deep (layers, 5 and 6)
pyramidal cells and a population of smooth inhibitory cells. Feedforward inputs – from the
thalamus – target all cell populations, but with an emphasis on inhibitory interneurons and
superficial and granular layers. Note the symmetrical deployment of inhibitory and
excitatory intrinsic connections that maintain a balance of excitation and inhibition.

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Figure 2.
This is a simplified schematic of the key intrinsic connections among excitatory (E) and
inhibitory (I) populations in granular (L4), supragranular (L1/2/3) and infragranular (L5/6)
layers. The excitatory interlaminar connections are based largely on Gilbert and Wiesel
(1983). Forward connections denote feedforward extrinsic corticocortical or thalamocortical
afferents that are reciprocated by backward or feedback connections. Anatomical and
functional data suggest that afferent input enters primarily into L4 and is conveyed to
superficial layers L2/3 that are rich in pyramidal cells, which project forward to the next
cortical area, forming a disynaptic route between thalamus and secondary cortical areas
(Callaway, 1998). Information from L2/3 is then sent to L5 and L6, which sends (intrinsic)
feedback projections back to L4 (Usrey and Fitzpatrick, 1996). L5 cells originate feedback
connections to earlier cortical areas as well as to the pulvinar, superior colliculus, and brain
stem. In summary, forward input is segregated by intrinsic connections into a superficial
forward stream and a deep backward stream. In this schematic, we have juxtaposed densely
interconnected excitatory and inhibitory populations within each layer.

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Figure 3.
This schematic shows an example of a generative model. Generative models describe how
(sensory) data are caused. In this figure, sensory states (blue circles on the periphery) are
generated by hidden variables (in the centre). The left panel shows the model as a
probabilistic graphical model, where unknown variables (hidden causes and states) are
associated with the nodes of a dependency graph and conditional dependencies are indicated
by arrows. Hidden states confer memory on the model by virtue of having dynamics, while
hidden causes connect nodes. A graphical model describes the conditional dependencies
among hidden variables generating data. These dependencies are typically modelled as
(differential) equations with nonlinear mappings and random fluctuations 
 with precision
(inverse variance) Π(i) (see the equations in the insert on the left). This allows one to specify
the precise form of the probabilistic generative model and leads to a simple and efficient
inversion scheme (predictive coding; see next figure). Here 
 denotes the set of hidden
causes that constitute the parents of sensory s̃
(i) or hidden x̃
(i) states. The ~ indicates states in
generalised coordinates of motion: x̃
 = (x, x′, x″,...). An intuitive version of the model is
shown on the right: here, we imagine that a singing bird is the cause of sensations, which –
through a cascade of dynamical hidden states – produces modality-specific consequences
(e.g., the auditory object of a bird song and the visual object of a song bird). These
intermediate causes are themselves (hierarchically) unpacked to generate sensory signals.
The generative model therefore maps from causes (e.g., concepts) to consequences (e.g.,
sensations), while its inversion corresponds to mapping from sensations to concepts or
representations. This inversion corresponds to perceptual synthesis – in which the generative
model is used to generate predictions. Note that this inversion implicitly resolves the binding
problem - by explaining multisensory cues with a single cause.

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Figure 4.
This figure describes the predictive coding scheme associated with a simple hierarchical
model shown on the left. In this model each node has a single parent. The ensuing inversion
or generalised predictive coding scheme is shown on the right. The key quantities in this
scheme are (conditional) expectations of the hidden states and causes and their associated
prediction errors. The basic architecture – implied by the inversion of the graphical
(hierarchical) model – suggests that prediction errors (caused by unpredicted fluctuations in
hidden variables) are passed up the hierarchy to update conditional expectations. These
conditional expectations now provide predictions that are passed down the hierarchy to form
prediction errors. We presume that the forward and backward message passing between
hierarchical levels is mediated by extrinsic (feedforward and feedback) connections.
Neuronal populations encoding conditional expectations and prediction errors now have to
be deployed in a canonical microcircuit to understand the computational logic of intrinsic
connections – within each level of the hierarchy – as shown in the next figure.

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Figure 5.
The left hand panel is the canonical microcircuit based on Haeusler and Maass (2007),
where we have removed inhibitory cells from the deep layers – because they have very little
interlaminar connectivity. The numbers denote connection strengths (mean amplitude of
PSPs measured at soma in mV) and connection probabilities (in parentheses) according to
Thomson et al. (2002). The right panel shows the proposed cortical microcircuit for
predictive coding, where the quantities of the previous figure have been associated with
various cell types. Here, prediction error populations are highlighted in pink. Inhibitory
connections are shown in red, while excitatory connections are in black. The dotted lines
refer to connections that are not present in the microcircuit on the left (but see Figure 2). In
this scheme, expectations (about causes and states) are assigned to (excitatory and
inhibitory) interneurons in the supragranular layers, which are passed to infragranular layers.
The corresponding prediction errors occupy granular layers, while superficial pyramidal
cells encode prediction errors that are sent forward to the next hierarchical level. Conditional
expectations and prediction errors on hidden causes are associated with excitatory cell types,
while the corresponding quantities for hidden states are assigned to inhibitory cells. Dark
circles indicate pyramidal cells. Finally, we have placed the precision of the feedforward
prediction errors against the superficial pyramidal cells. This quantity controls the
postsynaptic sensitivity or gain to (intrinsic and top-down) pre-synaptic inputs. We have
previously discussed this in terms of attentional modulation, which may be intimately linked
to the synchronisation of pre-synaptic inputs and ensuing postsynaptic responses (Fries et al
2001; Feldman and Friston, 2010).

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Figure 6.
This schematic illustrates the functional asymmetry between the spectral activity of
superficial and deep cells predicted theoretically. In this illustrative example, we have
ignored the effects of influences on the expectations of hidden causes (encoded by deep
pyramidal cells), other than the prediction error on causes (encoded by superficial pyramidal
cells). The lower panel shows the spectral density of deep pyramidal cell activity, given the
spectral density of superficial pyramidal cell activity in the upper panel. The equation
expresses the spectral density of the deep cells as a function of the spectral density of the
superficial cells; using Equation (2). This schematic is meant to illustrate how the relative
amounts of low (beta) and high (gamma) frequency activity in superficial and deep cells can
be explained by the evidence accumulation implicit in predictive coding.

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Table 1

Electrophysiological and neuroimaging findings consistent with predictive coding.

Prediction violated
Area studied
Neuronal expression of Prediction-
error

Study

Learned visual object pairings
Monkey inferotemporal cortex
(IT)

Enhanced firing rate
Meyer and Olson, 2011

Natural image statistics
Monkey V1, V2, V3
Enhanced firing rate
Hupé et al., 1998;
Bullier et al., 1996; Bair
et al., 2003

Repetitive auditory stream
Early human auditory cortex
Enhanced Event Related Potentials
(ERPs), enhanced gamma-band power

Garrido et al., 2007,
2009; Todorovic et al.,
2011

Coherence of visual form and
motion

Human V1, V2, V3, V4, V5/
MT

Enhanced BOLD response
Murray et al 2002;
Murray et al 2005;
Harrison et al., 2007

Audio-visual congruence of speech
Visual and auditory cortex
Gamma-band oscillatory activity
Arnal et al., 2011

Predictability of visual stimuli as a
function of attention

Human V1, V2, V3
Enhanced BOLD response when
unattended, reduced BOLD when
attended

Kok et al., 2011

Hierarchical expectations in
auditory sequences

Human temporal cortex
Enhanced Event Related Potentials
(ERPs)

Wacongne et al., 2011

Expected repetition (or
alternation) of face stimuli

FFA in fMRI, parietal and
central electrodes of EEG

Enhanced BOLD response, diminished
repetition suppression of ERP

Summerfield et al.,
2008, 2011

Apparent motion of visual
stimulus

V1
Enhanced BOLD response
Alink et al., 2010

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Table 2

The functional (computational) correlates of the anatomy and physiology of cortical hierarchies and their
extrinsic connections.

Anatomy and physiology
Functional correlates

Hierarchical organisation of cortical areas (Zeki and Shipp 1988;
Felleman and Van Essen, 1991; Barone et al., 2000; Vezoli, 2004)

Encoding of conditional dependencies in terms of a graphical
model (Mumford, 1992; Rao and Ballard, 1999; Friston 2008).

Distinct (laminar-specific) neuronal responses (Douglas et al., 1989;
Douglas and Martin, 1991)

Encoding expected states of the world (superficial pyramidal cells)
and prediction errors (deep pyramidal cells) (Mumford, 1992;
Friston 2008).

Distinct (laminar-specific) extrinsic connections (Zeki and Shipp
1988; Felleman and Van Essen, 1991; Barone et al., 2000; Vezoli, 2004;
Markov et al., 2011).

Forward connections convey prediction error (from superficial
pyramidal cells) and backward connections convey predictions
(from deep pyramidal cells) (Mumford, 1992; Friston 2008).

Reciprocal extrinsic connectivity (Zeki and Shipp 1988; Felleman and
Van Essen, 1991; Barone et al., 2000; Vezoli, 2004; Markov et al., 2011)

Recurrent dynamics are intrinsically stable because they are trying
to suppress prediction error (Crick and Koch 1998;; Friston 2008).

Feedback extrinsic connections are (driving and) modulatory
(Mignard and Malpeli 1991; Bullier et al., 1996; Sherman and Guillery
1998; Covic and Sherman, 2011; De Pasquale and Sherman, 2011).

Forwards (driving) and backwards (driving and modulatory)
connections mediate the (linear) influence of prediction errors and
the (linear and non-linear) construction of predictions (Friston
2008; 2010).

Feedback extrinsic connections are inhibitory (Murphy and Sillito,
1987; Sillito et al., 1993; Chu et al., 2003; Olsen et al. 2012; Meyer et al.,
2011; Wozny and Williams, 2011).

Top-down predictions suppress or counter prediction errors
produced by bottom up inputs (Mumford, 1992; Rao and Ballard,
1999; Friston 2008).

Differences in neuronal dynamics of superficial and deep layers (de
Kock et al., 2007; Sakata and Harris, 2009; Maier et al., 2010;
Bollimunta et al., 2011; Buffalo et al., 2011).

Principal cells elaborating predictions (deep pyramidal cells) may
show distinct (low-pass) dynamics, relative to those encoding error
(superficial pyramidal cells) (Friston 2008).

Dense intrinsic and horizontal connectivity (Thomson and Bannister,
2003; Katzel et al., 2010).

Lateral predictions and prediction errors mediating winnerless
competition and competitive lateral dependencies (Desimone,
1996; Friston 2010).

Predominance of nonlinear synaptic (dendritic and
neuromodulatory) infrastructure in superficial layers (Häusser and
Mel, 2003; London and Häusser, 2005; Gentet et al., 2012).

Required to scale prediction errors, in proportion to their precision,
affording a form of cortical bias or gain control that encodes
uncertainty (Feldman and Friston 2010; Spratling, 2008)

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